



'''simple docstring'''



# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class 						lowerCamelCase_				(       snake_case_      ):
						_lowerCAmelCase  : torch.FloatTensor
						_lowerCAmelCase  : Optional[torch.FloatTensor]						  =					None


def        UpperCAmelCase (    A	:					Dict       ,		A	:					Optional[Any]=0.999       ,		A	:					List[str]="cosine"       ,		):
							if alpha_transform_type == "cosine":

														def alpha_bar_fn(A	:					Tuple					):
																					return math.cos((t + 0.008) / 1.008 * math.pi / 2					) ** 2

							elif alpha_transform_type == "exp":

														def alpha_bar_fn(A	:					Any					):
																					return math.exp(t * -12.0					)

							else:
														raise ValueError(F"""Unsupported alpha_tranform_type: {alpha_transform_type}"""					)

							SCREAMING_SNAKE_CASE       :   List[str]         =      []
							for i in range(A					):
														SCREAMING_SNAKE_CASE       :   Tuple         =      i / num_diffusion_timesteps
														SCREAMING_SNAKE_CASE       :   List[Any]         =      (i + 1) / num_diffusion_timesteps
														betas.append(min(1 - alpha_bar_fn(A					) / alpha_bar_fn(A					)       ,		A					)					)
							return torch.tensor(A       ,		dtype=torch.floataa					)






class 						lowerCamelCase_				(       snake_case_     ,					snake_case_      ):
						_lowerCAmelCase  : str						  =					1







						@register_to_config
						def __init__(	self :   Tuple					,     lowerCAmelCase__ :   int = 10_00					,     lowerCAmelCase__ :   float = 0.0001					,     lowerCAmelCase__ :   float = 0.02					,     lowerCAmelCase__ :   str = "linear"					,     lowerCAmelCase__ :   Optional[Union[np.ndarray, List[float]]] = None					,     lowerCAmelCase__ :   bool = True					,     lowerCAmelCase__ :   bool = True					,     lowerCAmelCase__ :   int = 0					,     lowerCAmelCase__ :   str = "epsilon"					,     lowerCAmelCase__ :   float = 1.0					,     **lowerCAmelCase__ :   Any					,     ):

													"""simple docstring"""
													if kwargs.get('''set_alpha_to_one'''					,     lowerCAmelCase__					) is not None:
																				SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      (
																				    '''The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'''
																				)
																				deprecate('''set_alpha_to_one'''					,     '''1.0.0'''					,     lowerCAmelCase__					,     standard_warn=lowerCAmelCase__					)
																				SCREAMING_SNAKE_CASE       :   Any         =      kwargs['''set_alpha_to_one''']
													if trained_betas is not None:
																				SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      torch.tensor(lowerCAmelCase__					,     dtype=torch.floataa					)
													elif beta_schedule == "linear":
																				SCREAMING_SNAKE_CASE       :   Any         =      torch.linspace(lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__					,     dtype=torch.floataa					)
													elif beta_schedule == "scaled_linear":
																				# this schedule is very specific to the latent diffusion model.
																				SCREAMING_SNAKE_CASE       :   Any         =      (
																				    torch.linspace(beta_start**0.5					,     beta_end**0.5					,     lowerCAmelCase__					,     dtype=torch.floataa					) ** 2
																				)
													elif beta_schedule == "squaredcos_cap_v2":
																				# Glide cosine schedule
																				SCREAMING_SNAKE_CASE       :   Optional[int]         =      betas_for_alpha_bar(lowerCAmelCase__					)
													else:
																				raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""					)

													SCREAMING_SNAKE_CASE       :   Dict         =      1.0 - self.betas
													SCREAMING_SNAKE_CASE       :   Dict         =      torch.cumprod(self.alphas					,     dim=0					)

													# At every step in inverted ddim, we are looking into the next alphas_cumprod
													# For the final step, there is no next alphas_cumprod, and the index is out of bounds
													# `set_alpha_to_zero` decides whether we set this parameter simply to zero
													# in this case, self.step() just output the predicted noise
													# or whether we use the final alpha of the "non-previous" one.
													SCREAMING_SNAKE_CASE       :   Any         =      torch.tensor(0.0					) if set_alpha_to_zero else self.alphas_cumprod[-1]

													# standard deviation of the initial noise distribution
													SCREAMING_SNAKE_CASE       :   Dict         =      1.0

													# setable values
													SCREAMING_SNAKE_CASE       :   Dict         =      None
													SCREAMING_SNAKE_CASE       :   List[Any]         =      torch.from_numpy(np.arange(0					,     lowerCAmelCase__					).copy().astype(np.intaa					)					)







						def        __lowercase     (	self :   List[Any]					,     lowerCAmelCase__ :   torch.FloatTensor					,     lowerCAmelCase__ :   Optional[int] = None					):

													"""simple docstring"""
													return sample







						def        __lowercase     (	self :   Tuple					,     lowerCAmelCase__ :   int					,     lowerCAmelCase__ :   Union[str, torch.device] = None					):

													"""simple docstring"""

													if num_inference_steps > self.config.num_train_timesteps:
																				raise ValueError(
																				    F"""`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"""
																				    F""" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"""
																				    F""" maximal {self.config.num_train_timesteps} timesteps."""					)

													SCREAMING_SNAKE_CASE       :   Tuple         =      num_inference_steps
													SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      self.config.num_train_timesteps // self.num_inference_steps
													# creates integer timesteps by multiplying by ratio
													# casting to int to avoid issues when num_inference_step is power of 3
													SCREAMING_SNAKE_CASE       :   List[Any]         =      (np.arange(0					,     lowerCAmelCase__					) * step_ratio).round().copy().astype(np.intaa					)
													SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      torch.from_numpy(lowerCAmelCase__					).to(lowerCAmelCase__					)
													self.timesteps += self.config.steps_offset







						def        __lowercase     (	self :   Optional[int]					,     lowerCAmelCase__ :   torch.FloatTensor					,     lowerCAmelCase__ :   int					,     lowerCAmelCase__ :   torch.FloatTensor					,     lowerCAmelCase__ :   float = 0.0					,     lowerCAmelCase__ :   bool = False					,     lowerCAmelCase__ :   Optional[torch.FloatTensor] = None					,     lowerCAmelCase__ :   bool = True					,     ):

													"""simple docstring"""
													# 1. get previous step value (=t+1)
													SCREAMING_SNAKE_CASE       :   Dict         =      timestep + self.config.num_train_timesteps // self.num_inference_steps

													# 2. compute alphas, betas
													# change original implementation to exactly match noise levels for analogous forward process
													SCREAMING_SNAKE_CASE       :   Optional[int]         =      self.alphas_cumprod[timestep]
													SCREAMING_SNAKE_CASE       :   Dict         =      (
													    self.alphas_cumprod[prev_timestep]
													    if prev_timestep < self.config.num_train_timesteps
													    else self.final_alpha_cumprod
													)

													SCREAMING_SNAKE_CASE       :   Optional[Any]         =      1 - alpha_prod_t

													# 3. compute predicted original sample from predicted noise also called
													# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
													if self.config.prediction_type == "epsilon":
																				SCREAMING_SNAKE_CASE       :   Tuple         =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
																				SCREAMING_SNAKE_CASE       :   int         =      model_output
													elif self.config.prediction_type == "sample":
																				SCREAMING_SNAKE_CASE       :   Optional[Any]         =      model_output
																				SCREAMING_SNAKE_CASE       :   str         =      (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
													elif self.config.prediction_type == "v_prediction":
																				SCREAMING_SNAKE_CASE       :   Optional[int]         =      (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
																				SCREAMING_SNAKE_CASE       :   int         =      (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
													else:
																				raise ValueError(
																				    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"""
																				    ''' `v_prediction`'''					)

													# 4. Clip or threshold "predicted x_0"
													if self.config.clip_sample:
																				SCREAMING_SNAKE_CASE       :   Tuple         =      pred_original_sample.clamp(
																				    -self.config.clip_sample_range					,     self.config.clip_sample_range					)

													# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
													SCREAMING_SNAKE_CASE       :   List[Any]         =      (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

													# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
													SCREAMING_SNAKE_CASE       :   Optional[int]         =      alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

													if not return_dict:
																				return (prev_sample, pred_original_sample)
													return DDIMSchedulerOutput(prev_sample=lowerCAmelCase__					,     pred_original_sample=lowerCAmelCase__					)







						def __len__(	self :   Any					):

													"""simple docstring"""
													return self.config.num_train_timesteps









'''simple docstring'''



import os

lowerCAmelCase_  :							Union[str, Any]             =    {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
def        UpperCAmelCase (    A	:					str					):
							SCREAMING_SNAKE_CASE       :   str         =      0

							SCREAMING_SNAKE_CASE       :   List[str]         =      0
							while index < len(A					) - 1:
														SCREAMING_SNAKE_CASE       :   Dict         =      SYMBOLS[numerals[index]]
														SCREAMING_SNAKE_CASE       :   str         =      SYMBOLS[numerals[index + 1]]
														if current_value < next_value:
																					total_value -= current_value
														else:
																					total_value += current_value
														index += 1
							total_value += SYMBOLS[numerals[index]]

							return total_value
def        UpperCAmelCase (    A	:					int					):
							SCREAMING_SNAKE_CASE       :   Any         =      ''''''

							SCREAMING_SNAKE_CASE       :   Dict         =      num // 1000
							numerals += m_count * "M"
							num %= 1000

							SCREAMING_SNAKE_CASE       :   str         =      num // 100
							if c_count == 9:
														numerals += "CM"
														c_count -= 9
							elif c_count == 4:
														numerals += "CD"
														c_count -= 4
							if c_count >= 5:
														numerals += "D"
														c_count -= 5
							numerals += c_count * "C"
							num %= 100

							SCREAMING_SNAKE_CASE       :   Any         =      num // 10
							if x_count == 9:
														numerals += "XC"
														x_count -= 9
							elif x_count == 4:
														numerals += "XL"
														x_count -= 4
							if x_count >= 5:
														numerals += "L"
														x_count -= 5
							numerals += x_count * "X"
							num %= 10

							if num == 9:
														numerals += "IX"
														num -= 9
							elif num == 4:
														numerals += "IV"
														num -= 4
							if num >= 5:
														numerals += "V"
														num -= 5
							numerals += num * "I"

							return numerals
def        UpperCAmelCase (    A	:					str = "/p089_roman.txt"					):
							SCREAMING_SNAKE_CASE       :   List[str]         =      0

							with open(os.path.dirname(A					) + roman_numerals_filename					) as filea:
														SCREAMING_SNAKE_CASE       :   str         =      filea.readlines()

							for line in lines:
														SCREAMING_SNAKE_CASE       :   Any         =      line.strip()
														SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      parse_roman_numerals(A					)
														SCREAMING_SNAKE_CASE       :   Any         =      generate_roman_numerals(A					)
														savings += len(A					) - len(A					)

							return savings


if __name__ == "__main__":
							print(f'{solution() = }')




